Problem: Which of the following numbers is a factor of 72? ${5,7,10,12,14}$
Explanation: By definition, a factor of a number will divide evenly into that number. We can start by dividing $72$ by each of our answer choices. $72 \div 5 = 14\text{ R }2$ $72 \div 7 = 10\text{ R }2$ $72 \div 10 = 7\text{ R }2$ $72 \div 12 = 6$ $72 \div 14 = 5\text{ R }2$ The only answer choice that divides into $72$ with no remainder is $12$ $ 6$ $12$ $72$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $12$ are contained within the prime factors of $72$ $72 = 2\times2\times2\times3\times3 12 = 2\times2\times3$ Therefore the only factor of $72$ out of our choices is $12$. We can say that $72$ is divisible by $12$.